Articles
http://nur.nu.edu.kz:80/handle/123456789/4174
2021-10-22T13:35:47ZApproximation error of Fourier neural networks
http://nur.nu.edu.kz:80/handle/123456789/5845
Approximation error of Fourier neural networks
Zhumekenov, Abylay; Takhanov, Rustem; Castro, Alejandro J.; Assylbekov, Zhenisbek
The paper investigates approximation error of two-layer feedforward Fourier
Neural Networks (FNNs). Such networks are motivated by the approximation
properties of Fourier series. Several implementations of FNNs were proposed
since 1980s: byGallant andWhite, Silvescu, Tan, Zuo and Cai, and Liu. The main
focus of our work is Silvescu’s FNN, because its activation function does not fit
into the category of networks, where the linearly transformed input is exposed
to activation. The latter ones were extensively described by Hornik. In regard to
non-trivial Silvescu’s FNN, its convergence rate is proven to be of order O(1/n).
The paper continues investigating classes of functions approximated by Silvescu
FNN, which appeared to be from Schwartz space and space of positive definite
functions...
2021-03-23T00:00:00ZA COMPARISON OF MACHINE LEARNING ALGORITHMS IN PREDICTING LITHOFACIES: CASE STUDIES FROM NORWAY AND KAZAKHSTAN
http://nur.nu.edu.kz:80/handle/123456789/5726
A COMPARISON OF MACHINE LEARNING ALGORITHMS IN PREDICTING LITHOFACIES: CASE STUDIES FROM NORWAY AND KAZAKHSTAN
Merembayev, Timur; Kurmangaliyev, Darkhan; Bekbauov, Bakhbergen; Amanbek, Yerlan
Defining distinctive areas of the physical properties of rocks plays an important role in reservoir evaluation and hydrocarbon production as core data are challenging to obtain from all wells. In this work, we study the evaluation of lithofacies values using the machine learning algorithms in the determination of classification from various well log data of Kazakhstan and Norway. We also use the wavelet-transformed data in machine learning algorithms to identify geological properties from the well log data. Numerical results are presented for the multiple oil and gas reservoir data which contain more than 90 released wells from Norway and 10 wells from the Kazakhstan field. We have compared the the machine learning algorithms including KNN, Decision Tree, Random Forest, XGBoost, and LightGBM. The evaluation of the model score is conducted by using metrics such as accuracy, Hamming loss, and penalty matrix. In addition, the influence of the dataset features on the prediction is investigated using the machine learning algorithms. The result of research shows that the Random Forest model has the best score among considered algorithms. In addition, the results are consistent with outcome of the SHapley Additive exPlanations (SHAP) framework.
2021-03-29T00:00:00ZAPPROXIMATION ERROR OF FOURIER NEURAL NETWORKS
http://nur.nu.edu.kz:80/handle/123456789/5713
APPROXIMATION ERROR OF FOURIER NEURAL NETWORKS
Zhumekenov, Abylay; Takhanov, Rustem; Castro, Alejandro J.; Assylbekov, Zhenisbek
The paper investigates approximation error of two-layer feedforward Fourier Neural Networks (FNNs). Such networks are motivated by the approximation properties of Fourier series. Several implementations of FNNs were proposed since 1980s: by Gallant and White, Silvescu, Tan, Zuo and Cai, and Liu. The main focus of our work is Silvescu's FNN, because its activation function does not fit into the category of networks, where the linearly transformed input is exposed to activation. The latter ones were extensively described by Hornik. In regard to non-trivial Silvescu's FNN, its convergence rate is proven to be of order O(1/n). The paper continues investigating classes of functions approximated by Silvescu FNN, which appeared to be from Schwartz space and space of positive definite functions.
2021-03-23T00:00:00ZA MULTI-RHEOLOGY DESIGN METHOD OF SHEETING POLYMER EXTRUSION DIES BASED ON FLOW NETWORK AND THE WINTER–FRITZ DESIGN EQUATION
http://nur.nu.edu.kz:80/handle/123456789/5693
A MULTI-RHEOLOGY DESIGN METHOD OF SHEETING POLYMER EXTRUSION DIES BASED ON FLOW NETWORK AND THE WINTER–FRITZ DESIGN EQUATION
Razeghiyadaki, Amin; Wei, Dongming; Perveen, Asma; Zhang, Dichuan
In the polymer sheet processing industry, the primary objective when designing a coat-hanger die is to achieve a uniform velocity distribution at the exit of the extrusion die outlet. This velocity distribution depends on the internal flow channels of the die, rheological parameters and extrusion process conditions. As a result, coat-hanger dies are often designed for each polymer based on its individual rheological data and other conditions. A multi-rheology method based on a flow network model and the Winter–Fritz equation is proposed and implemented for the calculation, design and optimization of flat sheeting polymer extrusion dies. This method provides a fast and accurate algorithm to obtain die design geometries with constant wall-shear rates and optimal outlet velocity distributions. The geometric design when complemented and validated with fluid flow simulations could be applied for multi-rheological fluid models such as the power-law, Carreau– Yasuda and Cross. This method is applied to sheet dies with both circular-and rectangular-shaped manifolds for several rheological fluids. The designed geometrical parameters are obtained, and the associated fluid simulations are performed to demonstrate its favorable applicability without being limited to only the power-law rheology. The two such designed dies exhibit 32.9 and 21.5 percent improvement in flow uniformity compared to the previous methods for dies with circular and rectangular manifolds, respectively.
2021-06-10T00:00:00ZFACTORING WITH HINTS
http://nur.nu.edu.kz:80/handle/123456789/5668
FACTORING WITH HINTS
Sica, Francesco
We introduce a new approach to (deterministic) integer factorisation, which could be described in the cryptographically fashionable term of “factoring with hints”: we prove that, for any ϵ > 0, given the knowledge of the factorisations of O(N1/3+ϵ) terms surrounding N = pq product of two large primes, we can recover deterministically p and q in O(N1/3+ϵ) bit operations. This shows that the factorisations of close integers are non trivially related and that consequently one can expect more results along this line of thought...
2021-01-01T00:00:00ZEXPLICIT INVERSE OF NEAR TOEPLITZ PENTADIAGONAL MATRICES RELATED TO HIGHER ORDER DIFFERENCE OPERATORS
http://nur.nu.edu.kz:80/handle/123456789/5665
EXPLICIT INVERSE OF NEAR TOEPLITZ PENTADIAGONAL MATRICES RELATED TO HIGHER ORDER DIFFERENCE OPERATORS
Kurmanbek, Bakytzhan; Erlangga, Yogi; Amanbek, Yerlan
This paper analyzes the inverse of near Toeplitz pentadiagonal matrices, arising from a finite-difference approximation to the fourth-order nonlinear beam equation. Explicit non-recursive inverse matrix formulas and bounds of norms of the inverse matrix are derived for the clamped–free and clamped–clamped boundary conditions. The bound of norms is then used to construct a convergence bound for the fixed-point iteration of the form u=f(u) for solving the nonlinear equation. Numerical computations presented in this paper confirm the theoretical results.
2021-06-08T00:00:00Z